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A study of multilevel models with block circular  symmetric covariance structures
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the study of multilevel models with specific patterned covariance structures and addresses the issues of maximum likelihoodestimation. In particular, circular symmetric hierarchical datastructures are considered.

In the first paper (Paper I), we consider so-called dihedral block symmetrymodels and extend them to models which covariance structures reflects both circularity and exchangeability present in the data. The main contribution of Paper I are two derived patterns of the covariancematrices which characterizes models under consideration. The relationship between these two patterned covariance matrices was investigatedand it has been verified they are similar matrices. New expressions for the eigenvalues of block circular symmetric matrices are obtained which take into account the block structure. Paper II deals with estimation ofbalanced multilevel models with block circular symmetric covariance matrices. The spectral properties of such patterned covariance matrices are established. Maximum likelihood estimation is considered through the spectral decomposition of the patterned covariance matrix. The main results of Paper II concern the spectrum of the covariance matrix inthe model of interest and the existence of explicit maximum likelihood estimators for the covariance parameters.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University , 2011. , 22 p.
Keyword [en]
Block circular symmetry, Covariance matrix, Explicit solution, Maximum likelihood estimator, Multilevel model, Spectrum
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-81538ISBN: 978-91-633-9851-3 (print)OAI: oai:DiVA.org:su-81538DiVA: diva2:578475
Opponent
Supervisors
Available from: 2013-01-25 Created: 2012-10-25 Last updated: 2013-01-25Bibliographically approved
List of papers
1. Block Circular Symmetry in Multilevel Models
Open this publication in new window or tab >>Block Circular Symmetry in Multilevel Models
2011 (English)Report (Other academic)
Abstract [en]

Models that describe symmetries present in the error structure of observations have been widely used in dierent applications, with early examples from psychometric and medical research. The aim of this article is to study a multilevel model with a covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2011. 23 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 3
Keyword
Covariance matrix, Circular block symmetry, Multilevel model, Symmetry model, Spectrum
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-72075 (URN)
Available from: 2012-09-10 Created: 2012-02-02 Last updated: 2015-03-25Bibliographically approved
2. Estimation in multilevel models with block circular symmetric covariance structure
Open this publication in new window or tab >>Estimation in multilevel models with block circular symmetric covariance structure
2011 (English)Report (Other academic)
Abstract [en]

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

Publisher
17 p.
Series
Research Report, Department of Statistics, Stockholm University, ISSN 0280-7564 ; 4
Keyword
Circular block symmetry, Constrained model, Covariance matrix, Explicit solution, Maximum likelihood estimator, Multilevel model
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-72070 (URN)
Available from: 2012-09-10 Created: 2012-02-02 Last updated: 2013-01-25Bibliographically approved

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